“At least part of the motivation for any book is anger, and this book is no exception. I’m distressed by a society which depends so completely on mathematics and science and yet seems so indifferent to the innumeracy and scientific illiteracy of so many of its citizens…The desire to arouse a sense of numerical proportion and an appreciation for the irreducibly probabilistic nature of life—this, rather than anger, was the primary motivation for the book.” (Kindle Location 2272-2287)

Innumeracy has been my first taste of the wit and common sense of mathematician John Allen Paulos, who proposes in this book that the vast majority of human beings have no real concept of numbers and probabilities or the role they play in our everyday lives. He writes, “The discrepancies between our pretensions and reality are usually quite extensive, and since number and chance are among our ultimate reality principles, those who possess a keen grasp of these notions may see these discrepancies and incongruities with greater clarity and thus more easily become subject to feelings of absurdity” (Kindle Location 2283). Loosely translated: When you read the newspaper or consider the natural world around you, do the math. You’ll be shocked at the commonality of coincidence, the gullibility of the general public, and the silliness of pseudosciences.

Paulos certainly doesn’t profess to be a believer (in fact, he’s likely farther toward the other end of the spectrum), so one must read his essays with discernment, yet many of the points he brings to light (often humorously) are worth your consideration. Innumeracy (of course, the condition of being illiterate when it comes to numbers) is a rampant disease in our world, and here are just a few examples of how Paulos shows this to be true.

Innumeracy in Religion:

Now I know that Truth is truth. God’s Word being yet another “ultimate reality principle,” it is not hard for me to accept it by faith and then continue the lifelong process of understanding it more. After all, the belief in a single supernatural Being who lives outsides the boundaries of nature answers every question mankind could create; while the belief that God doesn’t exists opens every door to confusion from the very beginning (i.e. where did the point of matter come from before it exploded?).

That being said, Paulos does consider the “why”s behind the existence of so many world religions and their dogmatic followers, when the numbers tell us that “evidences” behind the validity of any belief system are often consumed with numerical incongruencies: “I don’t mean to advocate a rigid and dogmatic scientism or some kind of simpleminded atheism. There’s a long way from Adonai to I Don’t Know to I Deny—to adapt a line from poet Howard Nemerov—and plenty of room in the middle for reasonable people to feel comfortable” (Kindle Location 1106-1108)…”The point is that one can usually find loopholes which will enable one to hold on to whatever pet theory one fancies.” (Kindle Location 1113-1114)

Innumeracy in Daily Living:

Perhaps the most common-sensical portions of Innumeracy are those which deal with the innumeracy behind mankind’s greatest misconceptions. Take the common idea of coincidences, for example. Even Christians can get caught up in this, as evidenced by the popular question, “Why do bad things happen to good people?” In reality, this question could be restated as, “Why do bad things happen to anyone?” The curse from the Fall aside, Paulos responds by stating: “Bad things happen periodically, and they’re going to happen to somebody. Why not you?”(Kindle Location 1439-1440). The numbers prove that we’re all susceptible to chance occurrences. You might win the lottery by guessing the numbers, and you might get sucked into a sinkhole by walking down the road. Things happen, and they might happen to you. [Of course, as a believer I should note that, while I believe that “Things happen,” I do not believe that “Things just happen.” Therefore “chance occurrences” are actually either God’s ordaining events (death by sinkhole) or allowing nature to take its course (a rainstorm that soaks your clothes).]

Paulos doesn’t discuss only the concepts of chance and probability in Innumeracy, but in fact gets into many mathematical realities, for example averages and means. The Entertainment biz, for example, is rife with critics who thrive on discussing the causes for any particular celebrity’s successes and failures, yet Paulos responds that in reality, it’s nothing more than a universal rule of averages:

The sequel to a great movie is usually not as good as the original. The reason may not be the greed of the movie industry in cashing in on the first film’s popularity, but simply another instance of regression to the mean. A great season by a baseball player in his prime will likely be followed by a less impressive season. The same can be said of the novel after the best-seller, the album that follows the gold record, or the proverbial sophomore jinx. Regression to the mean is a widespread phenomenon, with instances just about everywhere you look. (1480-1484)

Innumeracy in Medicine:

The most important discussion in Innumeracy is how doctors and the Medical Machine thrive on society’s dependence upon narcotics to solve all their ailments, and how this dependence will continue no matter how well or how poorly the drugs actually work. In speaking to doctors who play off their patients’ innumeracy, Paulos explains a telling and terrible truth: “If the patient improves, you take credit; if he remains stable, your treatment stopped his downward course. On the other hand, if the patient worsens, the dosage or intensity of the treatment was not great enough; if he dies, he delayed too long in coming to you.” (1098-1100)

Innumeracy in Design:

In this final field I’d like to mention, John Allen Paulos inadvertently turns the tables on his readers by evidencing his own innumeracy concerning Intelligent Design, proving (to me at least) that no human being (even those mathematics professors among us) are immune to the disease. In fact, it boggles my mind how this mathematical genius could believe in the impossibility of “Evolution by Chance.” The numbers don’t add up, because “the numbers” (or the speck of matter) could never have simply popped into existence without a supernatural Influence, even given a billion-billion years…times a trillion. Paulos assumes that the impossible (i.e. spontaneous existence of physical elements and a source of energy) must have happened; and so, given time and “various combinations of possibilities,” “intelligence developed naturally” here on earth. Here’s his comment in full:

If intelligence developed naturally on earth, it is difficult to see why the same process wouldn’t have occurred elsewhere. What’s needed is a system of physical elements capable of many different combinations, and a source of energy through the system. The energy flux causes the system to “explore” various combinations of possibilities, until a small collection of stable, complex, energy-storing molecules develops, followed by the chemical evolution of more complex compounds, including some amino acids, from which proteins are constructed. Eventually, primitive life develops, and then shopping malls. (Kindle Location 1055-59)

Lunacy. For all the wonderful things I learned in this book about my own failures to “do the math” concerning everything around me that I take for granted, I still recognize that John Allen Paulos is a man—a man who understands numbers and all they can teach us, but an imperfect (and likely godless) man nonetheless.

Job 38 is a chapter filled with a list of natural wonders that God has performed since the beginning of Creation, and it’s interesting to note that advancements in science and technology have allowed modern mankind to replicate about half of them. Yet snuggled away inside that very chapter is a question from God that is so telling, I think that all mankind must consider it, for in answering it, we answer all of our deepest questions: “Who has put wisdom in the inward parts or given understanding to the mind?” (Job 38:36).